Chapter 2 Notes: Mixtures, Atomic Structure, Isotopes, and Mass Spectrometry

Heterogeneous Mixture – a mixture that is not the same throughout.
Homogeneous Mixture (Solution) – a mixture that is the same throughout.
Physical Properties: can be measured or observed without changing the composition or identity of the substance
- Examples: Density, conductivity, melting point, color, hardness
Chemical Properties: describe how a substance may change or react to form other substances
- Examples: Flammability, corrosivity, reactivity
Chemical reactions occur during chemical changes.

Electron is the lightest particle (basically weightless).
Electric current definition:
- 1 C/s = 1 A
- In symbols: 1\ \text{C/s} = 1\ \text{A}
Periodic table organization:
- Elements arranged in order of increasing number of protons (atomic number, Z).
- Not all elements have the same number of neutrons as protons; this leads to isotopes.
Protons, neutrons, and electrons:
- Protons: positively charged
- Neutrons: neutral
- Electrons: negatively charged
Hydrogen vs Helium (as mentioned):
- Hydrogen has 1 proton and, in its most common isotope, 0 neutrons (doesn’t require a neutron).
- Helium has 2 protons and typically 2 neutrons (2 of each, for the common stable isotope).
Isotope: atoms with the same number of protons (same atomic number Z) but a different number of neutrons.
Atomic symbols and notation:
- Mass Number A = number of protons + number of neutrons (A = Z + N)
- Atomic Number Z = number of protons (p^+)
- In neutral atoms, the number of electrons e^- equals the number of protons: e^- = p^+ = Z
Example: ^{48}_{22}Ti
- Protons = 22
- Neutrons = 26 (since A - Z = 48 - 22 = 26)
- Electrons = 22 (in a neutral atom)
- Ion notation example: ^{51}_{23}V^{4+}
- Z = 23; A = 51; N = A - Z = 28
- Charge = +4; electrons = Z − 4 = 19
- Another explicit ion example (as given):
- For ^{51}_{23}V^{4+}, electrons = 19 (since 23 - 4 = 19)

Ions: atoms that have gained or lost electrons
- Cations are positive ions, typically formed by metals (example: Mg^{2+})
- Anions are negative ions, typically formed by non-metals (example: O^{2-})
If an ion has a + charge, it has fewer electrons than protons; if it has a - charge, it has more electrons than protons.

Isotopes: atoms with the same number of protons (same Z) but different numbers of neutrons (different A).
Some isotopes are more abundant than others.
Mass Spectrometry: a technique where ionized isotopes are separated due to differences in their mass-to-charge ratio (m/z).
- Relative abundances can be determined from the separation and intensities in a mass spectrum.

Atomic weight (atomic mass) amu is a weighted average of the masses of all isotopes of an element.
amu = atomic mass = weighted average of all isotopes
Weighted average depends on the isotopic abundances.
Calculation principle (conceptual):
- If an element has isotopes i with mass number Ai and fractional abundance fi (where \sum f_i = 1), then:
- \text{amu} = \sumi fi \cdot A_i
Important practical note:
- Do not simply average masses without weights; use the weighted average according to each isotope’s abundance.
Mass spectrometry context:
- Ionized isotopes are separated by their mass-to-charge ratio \frac{m}{z}, where m is the mass and z is the charge on the ion.
- The spectrum provides information about isotopic composition and relative abundances.

Mass number: A = Z + N
Atomic number: Z = p^+
Neutral atom electrons: e^- = Z
Ion electrons: for an ion with charge q (positive if a cation, negative if an anion),
- e^- = Z - q where q is the net positive charge (e.g., for a 4+ cation, q = +4, so e^- = Z - 4).
Isotope notation (example): ^{A}_{Z}\text{X} where X is the element, A is mass number, Z is atomic number.
Relative atomic mass (atomic weight):
- \text{amu} = \sumi fi \cdot Ai, with \sumi f_i = 1.
Mass-to-charge ratio in mass spectrometry:
- \frac{m}{z} where m is mass of the ion and z is its charge number.

Example 1: ^{48}_{22}Ti
- Z = 22; A = 48; N = A - Z = 26; e^- (neutral) = 22.
Example 2: ^{51}_{23}V^{4+}
- Z = 23; A = 51; N = 28; charge = +4; e^- = 23 - 4 = 19.
Example 3: Hydrogen vs Helium isotopes
- Hydrogen most common isotope: Z = 1, N = 0, A = 1; e^- = 1 in neutral form.
- Helium typical stable isotope: Z = 2, N = 2, A = 4; e^- = 2 in neutral form.
Isotopic abundance and amu calculation in practice:
- If Magnesium has two main isotopes, say ^{24}Mg (abundance a) and ^{26}Mg (abundance b), with masses 24 and 26 respectively, then amu ≈ a×24 + b×26, where a + b ≈ 1.
Mass spectrometry relevance:
- Used to determine isotopic composition, calculate atomic weights, and identify elements in mixtures.

The periodic table is organized by increasing proton number (Z).
Isotopes differ in neutron number but share the same Z.
Atomic weight is a weighted average of isotopic masses based on natural abundances.
Ions are charged species formed by loss or gain of electrons; their electron count depends on the net charge.
Mass spectrometry relies on mass-to-charge differences to separate isotopes and determine abundances.